A few families took a trip to an amusement park together. Tickets cost $$7.50$ each for adults and $$2.00$ each for kids, and the group paid $$31.00$ in total. There were $6$ fewer adults than kids in the group. Find the number of adults and kids on the trip.
Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${7.5x+2y = 31}$ ${x = y-6}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-6}$ for $x$ in the first equation. ${7.5}{(y-6)}{+ 2y = 31}$ Simplify and solve for $y$ $ 7.5y-45 + 2y = 31 $ $ 9.5y-45 = 31 $ $ 9.5y = 76 $ $ y = \dfrac{76}{9.5} $ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into ${x = y-6}$ to find $x$ ${x = }{(8)}{ - 6}$ ${x = 2}$ You can also plug ${y = 8}$ into ${7.5x+2y = 31}$ and get the same answer for $x$ ${7.5x + 2}{(8)}{= 31}$ ${x = 2}$ There were $2$ adults and $8$ kids.